8350 is a superior CPU. You can go to cheaper alternative like FX 6300 if it is sufficient for your needs. FX 6300 works well with R9 270. 8320 also. You can overclokc your FX 6300 and get more performance out of it.
If you ask me 8350 is a bit of overkill for R9 270
The fx-6300 is around $120-130 (aud im aussie) the fx-8320 around $100-110 and the 8350 is $130-150, i could get the 6300 depending on its performance and get a ssd with that $100 saved.